Precipitation Strengthening by Induction Treatment in High Strength Low Carbon Microalloyed Hot-Rolled Plates

Metallurgical and Materials Transactions A - The use of microalloyed steels in the production of thick plates is expanding due to the possibility of achieving attractive combinations of strength...     

On the asymptotic performance analysis of subspace DOA estimation in the presence of modeling errors: case of MUSIC

This paper provides a new analytic expression of the bias and RMS error (root mean square) error of the estimated direction of arrival (DOA) in the presence of modeling errors. In , first-order approximations of the RMS error are derived, which are accurate for small enough perturbations. However, the previously available expressions are not able to capture the behavior of the estimation algorithm into the threshold region. In order to fill this gap, we provide a second-order performance analysis, which is valid in a larger interval of modeling errors. To this end, it is shown that the DOA estimation error for each signal source can be expressed as a ratio of Hermitian forms, with a stochastic vector containing the modeling error. Then, an analytic expression for the moments of such a Hermitian forms ratio is provided. Finally, a closed-form expression for the performance (bias and RMS error) is derived. Simulation results indicate that the new result is accurate into the region where the algorithm breaks down.     

Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis

Recently, a new adaptive scheme [Conte (1995), Gini (1997)] has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non-Gaussian noise. This latter has been modeled by compound-Gaussian noise, which is the product c of the square root of a positive unknown variable tau (deterministic or random) and an independent Gaussian vector x, c=radictaux. Because of the implicit algebraic structure of the equation to solve, we called the corresponding solution, the fixed point (FP) estimate. When tau is assumed deterministic and unknown, the FP is the exact maximum-likelihood (ML) estimate of the noise covariance structure, while when tau is a positive random variable, the FP is an approximate maximum likelihood (AML). This estimate has been already used for its excellent statistical properties without proofs of its existence and uniqueness. The major contribution of this paper is to fill these gaps. Our derivation is based on some likelihood functions general properties like homogeneity and can be easily adapted to other recursive contexts. Moreover, the corresponding iterative algorithm used for the FP estimate practical determination is also analyzed and we show the convergence of this recursive scheme, ensured whatever the initialization.     

Performance Analysis of Covariance Matrix Estimates in Impulsive Noise

This paper deals with covariance matrix estimates in impulsive noise environments. Physical models based on compound noise modeling [spherically invariant random vectors (SIRV), compound Gaussian processes] allow to correctly describe reality (e.g., range power variations or clutter transitions areas in radar problems). However, these models depend on several unknown parameters (covariance matrix, statistical distribution of the texture, disturbance parameters) that have to be estimated. Based on these noise models, this paper presents a complete analysis of the main covariance matrix estimates used in the literature. Four estimates are studied: the well-known sample covariance matrix M_SCM and a normalized version M_N, the fixed-point (FP) estimate M_FP, and a theoretical benchmark M_TFP. Among these estimates, the only one of practical interest in impulsive noise is the FP. The three others, which could be used in a Gaussian context, are, in this paper, only of academic interest, i.e., for comparison with the FP. A statistical study of these estimates is performed through bias analysis, consistency, and asymptotic distribution. This study allows to compare the performance of the estimates and to establish simple relationships between them. Finally, theoretical results are emphasized by several simulations corresponding to real situations.     

Maximum Likelihood-Based Direction-of-Arrival Estimator for Discrete Sources

This paper addresses the problem of direction-of-arrival (DOA) parameter estimation in array processing when the signals are inherently discrete, which is the case mainly in the digital communication context. Based on the particular structure of the signal space in the data model, a maximum likelihood-based approach is introduced. The strategy consists in transforming the parameter estimation problem into a decision task. It is shown through numerical simulations that the proposed solution closely follows the performance limit given by the Cramér–Rao bound. Some important features of the technique are as follows: (i) it is capable of handling any number of sources, provided that the number of sensors is greater than or equal to two and the number of snapshots is sufficiently greater than the cardinality of the signal space; (ii) the estimation quality is not affected by the angle and phase separation; and (iii) it offers the possibility to deal with uncalibrated arrays.     

Threshold performance analysis of maximum likelihood DOA estimation

The purpose of this paper is to investigate the nonasymptotic behavior of the maximum likelihood method in the context of lacunar array processing. We derive an analytical expression of the maximum likelihood mean square error, which is now valid for all signal-to-noise ratio (SNR) ranges. We also provide an analysis of the SNR threshold phenomena, which allows us to derive closed-form formulas for the threshold values. Computer simulations confirm the validity of the theoretical investigations.     

On the Resolution Probability of MUSIC in Presence of Modeling Errors

The problem of resolving closely spaced signal sources using an antenna array remains a difficult one, although several estimation methods are available in the literature. When the array correlation matrix is known, the resolution capability of subspace algorithms is infinitely high. However, in the presence of modeling errors the resolution deteriorates, even for a known correlation matrix. In this paper, we analyze the MUSIC method, by way of three different definitions of the resolution. Assuming Gaussian circular random modeling errors, we determine the corresponding expressions of the probability of source resolution versus the model mismatch. A first series of simulations validates the mathematical expression of the three resolution probabilities. A second series of simulations is used to select among them the tightest one to the empirical one. The results are useful, e.g., for determining the necessary antenna calibration accuracy to achieve a target performance.     

High resolution approach for the localization of buried defects in the multi-frequency eddy current imaging of metallic structures

A high resolution approach is proposed to quantitatively estimate the depth of defects buried in planar metallic structures. This approach associates a multiple signal characterization (MUSIC) algorithm with an original eddy current imager. The interactions of the eddy currents and the defects are modelled by a set of virtual magnetic sources propagating in a spherical manner up to the surface of the structure. The defect localization is carried out using the MUSIC algorithm, applied to the multi-frequency observation of the magnetic field distribution at the surface of the structure. Accurate results obtained on simulated and experimental data relative to defects buried down to 5.4 mm in an aluminium layered structure validate the approach.     

Parametric spectral moments estimation for wind profiling radar

The purpose of this work is the estimation of Doppler echoes spectral moments. In case of strong overlapping, Fourier-like techniques provide poor results because of the lack of resolution. We propose the use of stochastic maximum-likelihood (SML) and subspace-based methods (WPSF algorithm) for a joint estimation of spectral moments. The statistical performances (theoretical and empirical by Monte Carlo simulations) of estimators are compared with the Cramer-Rao lower bound. The results of tests performed on very high frequency (VHF) times series obtained during Thunderstorm, Arecibo, PR during September and October 1998 validate the model and algorithms and confirm the interest of both approaches.     

Weiss-Weinstein bound for MIMO radar with colocated linear arrays for SNR threshold prediction

Several works have suggested that a multi-input multi-output (MIMO) radar system offers improvement in terms of performance in comparison with classical phased-array radar. However, under the widely spread assumption of a uniform a priori distribution for one parameter of interest, there is no result concerning lower bounds on the mean-square error in the case of a Gaussian observation model with parameterized mean. This Fast Communication fills this lack by using the Weiss-Weinstein bound (WWB) which can be calculated under this difficult scenario. As we will show, the proposed bound for MIMO Radar with colocated linear arrays has no closed-form expression. To solve this problem, we propose a closed-form approximation that, as we will show by simulations, is close to the actual bound. This approximated bound is then analyzed for a design purpose in terms of array geometry. Simulations confirm the good ability of the proposed bound to predict the mean square error (MSE) of the maximum a posteriori (MAP) in all ranges of SNR. Particularly, the tightness of the bound to predict the SNR threshold effect is shown.